Calculate the final selling price to the nearest cent and markdown percent to the nearest hundredth percent: original selling price first markdown second markdown markup final markdown $5,600 35% 25% 18% 15% i figured out the final selling price $2738.19 but don't understand how to calculate the markdown percent

There are a couple of ways you can go at this. One way is to look at the price multipliers. For a markdown of d, the price is multiplied by 1-d. For a markup of u, the price is multiplied by 1+u. Your original price is multiplied by ...
  35% markdown: (1 - 0.35) = 0.65
  25% markdown: (1 - 0.25) = 0.75
  18% markup: (1 + 0.18) = 1.18
  15% markdown: (1 - 0.15) = 0.85

The product of all these multipliers is
  0.65×0.75×1.18×0.85 = 0.4889625

As you note, $5600×0.4889625 = $2738.19.

Since this multiplier is 1-d, we can find d as
  1 - d = 0.4889625
  d = 1 - 0.4889625 = 0.5110375
The markdown percentage is this number times 100%:
  markdown% ≈ 51.1%


Alternatively, you can work with your final value to find the percentage change from the original.
  percent change = ((final value) - (original value))/(original value) × 100%
    = (2738.19 - 5600)/5600 × 100%
    = -2861.81/5600 × 100%
    = -0.5110375 × 100% . . . . . . . this should look familiar
  percent change ≈ -51.1%

When the change is negative, it is a markdown (not a markup).
The markdown is 51.1%.